Best Estimate Plus Uncertainty Research Articles

Best Estimate Plus Uncertainty Analysis of Station Blackout Transient in Pool-Type Research Reactor

Simulation of a station blackout (SBO) scenario was carried out for an open pool–type nuclear research reactor. The SBO transient was analyzed using the best estimate (BE) thermal-hydraulic code RELAP5/MOD3.2 to evaluate the performance of safety systems and inherent thermal inertia provided by the reactor pool in ensuring adequate core cooling during a prolonged SBO condition lasting up to 7 days. This encompasses assessment of cooling provided by battery-operated auxiliary pumps in the initial phase followed by setup of the natural convection cooling mode for the extended period. Best Estimate Plus Uncertainty (BEPU) methodology was applied for assessment of safety margins. This involved estimation of required simulations using the Wilks first-order formulation to achieve results within the tolerance limit of 95/95. Identification of relevant uncertainties and their propagation was carried out; subsequently, a case matrix for 59 simulation runs was generated using the Latin hypercube sampling method. The upper/lower bounds of uncertainty results were analyzed and compared with the BE code results. Later, sensitivity analysis was carried out using sensitivity coefficients generated using the Pearson and Spearman coefficient. The results show that the values of the crucial thermal-hydraulic parameters obtained with the tolerance limit of 95/95 met the acceptance criteria, with adequate safety margins.

Safety evaluation of Multiple Steam Generator Tube rupture accident using the best estimate plus uncertainty approach

Following the disaster in Fukushima Nuclear Power Plant (NPP) in 2011, the awareness of securing the safety of NPP under extreme events has been raised. For this purpose, the concept of Design Extension Conditions (DECs) was introduced, to enhance the plant’s capability to withstand events that are more severe than Design Basis Accidents (DBA), such as Multiple Steam Generator Tube Rupture (MSGTR) accident, given its rapid progression and significant potential for large release of radioactive materials to the environment. It is worth noting that MSGTR has never occurred during the commercial operation of nuclear power plant, therefore the knowledge of consequences of the event and potential mitigation strategy is limited. In this study, a postulated MSGTR (simultaneous rupture of 5 U-tubes in a single SG) accident is analysed using the best-estimate thermal hydraulics code RELAP5/SCDAPSIM/MOD3.4. The main focus of this work is evaluation of appropriate operator mitigation actions under various inherent uncertainties. To this end, the best estimate plus uncertainty (BEPU) approach is adopted, whereby RELAP5/SCDAPSIM/MOD3.4 was coupled to the statistical analysis software, DAKOTA, to conduct the uncertainty quantification (UQ). Using BEPU analysis, an ensemble of system responses under various epistemic and aleatory uncertainties is obtained and used to validate the efficacy of operator actions in bringing the plant to a safe shutdown condition.

Safety margin quantification by integrating probabilistic and deterministic safety assessments — Application to design extension conditions

Various safety analysis methods have been used over the years to quantify safety margins: at the start by Deterministic Safety Analysis (DSA) with conservative models or best estimate models and “bounding” assumptions; then by the Best Estimate Plus Uncertainty (BEPU) approach which takes into account uncertainties related to physical and modelling parameters; and recently by the Extended BEPU (EBEPU) approach with the intention of incorporating information from Probabilistic Safety Assessment (PSA).By combining probabilistic and deterministic safety assessments while taking into consideration a wide variety of uncertainties, the current work aims at the development of an Integrated Safety Margin Quantification (ISMQ) technique to extend the scope of existing approaches. Multiple aspects of the “safety margin” can be handled by this ISMQ methodology, including pertinent Initiating Events (IE) and sequences, the distance between best-estimate load and safety limit, and the likelihood of exceeding the safety limit.Together with the suggested methodology, an industrial application on Design Extension Conditions (DEC) of a typical Generation II 1000 MWe Pressurized Water Reactor (PWR) is presented to illustrate the approach and the anticipated outcomes. This ISMQ methodology is also applicable for safety analyses of other reactor designs including Small Modular Reactors (SMRs).

Time-Series Forecasting of a Typical PWR Undergoing Large Break LOCA

In this work, a machine learning (ML) metamodel is developed for the time-series forecasting of a typical nuclear power plant response undergoing a loss of coolant accident (LOCA). The plant model of choice is based on the APR1400 nuclear reactor. The key systems and components of APR1400 relevant to the investigated scenario are modelled using the thermal-hydraulic code, RELAP5/MOD3.4, following the description published in the design control document. The model is tested under a spectrum of initial and boundary conditions via propagation of key uncertain parameters (UPs) which are derived from the phenomena identification and ranking table (PIRT). This is achieved by loosely coupling RELAP5/MOD3.4 with the statistical tool, Dakota. The most probable nuclear power plant (NPP) response was calculated using the best estimate plus uncertainty (BEPU) approach. Next, the database generated from the NPP system response was used as an input for the ML model. The NPP system response was represented by peak cladding temperature (PCT), safety injection system (SIT), mass flow rate, reactor power, and primary system pressure. In this research, two regression models were tested with reasonably good performance, namely, the gated recurrent unit (GRU) and the long short-term memory (LSTM).

Spanish contribution to the development and application of best estimate plus uncertainty methodologies: Past, present and future

Best-Estimate Plus Uncertainty (BEPU) nuclear safety analysis is an approach widely used in the field of nuclear engineering and reactor safety assessment. It aims to provide a more realistic assessment of reactor safety by considering a combination of best-estimate models and the quantification of the uncertainty of the input and code data.The Spanish research community in collaboration with the regulatory body and the industry has substantially contributed to the development and application of BEPU methodologies by taking an active role in the international joint efforts. The present article provides an overview of the key contributions performed by Spanish institutions. Many of the activities performed in BEPU are dedicated to the thermal-hydraulics field where Spanish researchers have contributed to both the development of forward and inverse uncertainty propagation methods. On the other hand, BEPU related works have also been performed in several other disciplines such as neutron-kinetics, fuel thermo-mechanics, computational fluid dynamics, containment, severe accident and in coupled multi-physics applications. All these contributions are first summarized to set the framework for a final section that provides the future challenges that lay ahead in the upcoming years in relation to the implementation of BEPU methods.

Validation and uncertainty analysis of ASTEC in early degradation phase against QUENCH-06 experiment

Severe Accident (SA) integral codes, such as the Accident Source Term Evaluation Code (ASTEC) developed by IRSN, are used to simulate the phenomena occurring during accident progression in Nuclear Power Plants (NPPs) up to the source term evaluation. Code validation against experimental data is fundamental to carry out deterministic safety analysis and apply these codes to NPPs. In addition, in the Best Estimate Plus Uncertainty (BEPU) framework, the quantification of the results uncertainty is needed. In the framework of the IAEA CRP I31033 “Advancing the State-of-Practice in Uncertainty and Sensitivity Methodologies for Severe Accident Analysis in Water-Cooled Reactors”, the QUENCH test-6 experiment, conducted at KIT, has been selected to develop an uncertainty analysis using the ASTEC v2.2b code. The accuracy of the best-estimate ASTEC simulation was evaluated with the Fast Fourier Transform Based Method (FFTBM) against the experimental data. Then, the uncertainty of the code results was quantified by using the probabilistic propagation of input uncertainties method, through the coupling of ASTEC with RAVEN (Risk Analysis and Virtual Environment). Beyond identifying the main sources of uncertainty affecting the simulated test, the outcomes of the work also include some general discussion on the uncertainty propagation in a SA sequence.

Time-series forecasting of a typical PWR system response under Control Element Assembly withdrawal at full power

To expedite the decision-making process under Nuclear Power Plant (NPP) accident conditions, at a reduced computational cost, a Machine Learning (ML) time-series meta-model is proposed to map the relationships between the NPP's real-time parameters to its transient response and hence forecast its future response. To this end, three variations of Recurrent Neural Networks (RNNs), namely: the Long-Short-Term-Memory (LSTM), Gated Recurrent Unit (GRU) and a series combination of a convolutional neural network (CNN) with LSTM were developed. The NPP response was simulated using the thermal hydraulics best estimate code, MARS-KS, and cross-validated against the Design Control Document (DCD) of APR1400. The time-series database required to train, test, and validate the time-series Machine Learning (ML) expert algorithm was acquired by coupling DAKOTA software with the best estimate thermal hydraulics system code, MARS-KS to conduct a Best Estimate Plus Uncertainty (BEPU) analysis. The Monte-Carlo random propagation approach and the Latin Hypercube Sampling technique were used to sample and propagate key uncertain parameters until a statistically significant sample of the NPP transient responses was achieved. All three RNN models were developed and optimized with the help of the Talos tool, and were found to exhibit reasonable performance in forecasting the key most probable NPP transient responses, Furthermore, the uncertainty of the ML predictions was assessed by integrating a Bayesian Neural Network (BNN) with the LSTM model. The prediction accuracy ranged from 86% to 96%, when evaluated on an unseen test dataset. Based on a voting system with five performance metrics (MAE, MSE, RMSE, R2 and Accuracy) the LSTM model and its derivative CNN+LSTM outperformed the GRU model; while the CNN +LSTM is found to be the most computationally efficient.

Analysis of Control Element Assembly Withdrawal at Full Power Accident Scenario Using a Hybrid Conservative and BEPU Approach

Reactivity Initiated Accident (RIA) scenarios require special attention using advanced simulation techniques due to their complexity and importance for nuclear power plant (NPP) safety. While the conservative approach has traditionally been used for safety analysis, it may lead to unrealistic results which calls for the use of best estimate plus uncertainty (BEPU) approach, especially with the current advances in computational power which makes the BEPU analysis feasible. In this work an Uncontrolled Control Element Assembly (CEA) Withdrawal at Full Power accident scenario is analyzed using the BEPU approach by loosely coupling the thermal hydraulics best-estimate system code (RELAP5/SCDAPSIM/MOD3.4) to the statistical analysis software (DAKOTA) using a Python interface. Results from the BEPU analysis indicate that a realistic treatment of the accident scenario yields a larger safety margin and is therefore encouraged for accident analysis as it may enable more economic and flexible operation.

Uncertainty quantification for severe-accident reactor modelling: Set-up and first results of the Horizon-2020 project MUSA

The current Horizon-2020 project on “Management and Uncertainties of Severe Accidents (MUSA)” aims at applying Uncertainty Quantification (UQ) in the modelling of Severe Accidents (SA), particularly in predicting the radiological source term of mitigated and unmitigated accident reactor scenarios. A selected number of severe accident sequences of different nuclear power plant designs (e.g. PWR, VVER, and BWR) are addressed.The application of the Best Estimate Plus Uncertainty (BEPU) methodology to reactor accident scenarios requires a number of key steps: (i) the selection of severe accident sequences for each reactor design; (ii) the development of a reference input model for the specific design and SA-code; (iii) the definition of the figures of merit for the UQ-analysis; (iv) the selection of a list of uncertain model parameters to be investigated; (v) the choice of a statistical tool to propagate input deck uncertainties; (vi) the selection of a feasible approach (i.e., Monte Carlo versus order statistics) to address UQ by using a statistical software (i.e., UQ-tools DAKOTA, SUSA, URANIE, etc.); (vii) the running phase to achieve a high number of successful realizations with the SA codes; and, (viii) the statistical evaluation of the results (i.e., sensitivity analysis).This paper describes each of these steps such as settled in the reactor applications work package of the EU MUSA project and pays particular attention to the choices made by partners. It presents preliminary results also with an emphasis on the major challenges posed by BEPU application in the field of SA analysis.

Using machine learning to forecast and assess the uncertainty in the response of a typical PWR undergoing a steam generator tube rupture accident

In this work, a multivariate time-series machine learning meta-model is developed to predict the transient response of a typical nuclear power plant (NPP) undergoing a steam generator tube rupture (SGTR). The model employs Recurrent Neural Networks (RNNs), including the Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), and a hybrid CNN-LSTM model. To address the uncertainty inherent in such predictions, a Bayesian Neural Network (BNN) was implemented. The models were trained using a database generated by the Best Estimate Plus Uncertainty (BEPU) methodology; coupling the thermal hydraulics code, RELAP5/SCDAP/MOD3.4 to the statistical tool, DAKOTA, to predict the variation in system response under various operational and phenomenological uncertainties. The RNN models successfully captures the underlying characteristics of the data with reasonable accuracy, and the BNN-LSTM approach offers an additional layer of insight into the level of uncertainty associated with the predictions. The results demonstrate that LSTM outperforms GRU, while the hybrid CNN-LSTM model is computationally the most efficient. This study aims to gain a better understanding of the capabilities and limitations of machine learning models in the context of nuclear safety. By expanding the application of ML models to more severe accident scenarios, where operators are under extreme stress and prone to errors, ML models can provide valuable support and act as expert systems to assist in decision-making while minimizing the chances of human error.

Uncertainties impact on the major FOMs for severe accidents in CANDU 6 nuclear power plant

In the nuclear safety studies, a new trend refers to the evaluation of uncertainties as a mandatory component of best-estimate safety analysis which is a modern and technically consistent approach being known as BEPU (Best Estimate Plus Uncertainty).The major objectives of this study consist in performing a study of uncertainties/sensitivities of the major analysis results for a generic CANDU 6 Nuclear Power Plant during Station Blackout (SBO) progression to understand and characterize the sources of uncertainties and their effects on the key figure-of-merits (FOMs) predictions in severe accidents (SA).The FOMs of interest are hydrogen mass generation and event timings such as the first fuel channel failure time, beginning of the core disassembly time, core collapse time and calandria vessel failure time. The outcomes of the study, will allow an improvement of capabilities and expertise to perform uncertainty and sensitivity analysis with severe accident codes for CANDU 6 Nuclear Power Plant.

Small Modular Reactors Licensing Process Based on BEPU Approach: Status and Perspective

The competitiveness of small modular reactors (SMRs) has been planned based on design simplification, short construction time, passive safety systems, and enabling self-financing by ramp-up construction. Due to the global energy challenges, SMRs have received pervasive attention from a wide range of researchers, designers, developers, stakeholders, and customers. Besides the many advantages related to the design of SMRs, there are challenges ahead of these reactors. SMR licensing is one of the most critical challenges in the front deployment of these reactors. This challenge stems from innovations in SMR designs and systems, such as modularity or deployment for desalination, energy storage, hydrogen production, process heat, and district heating. Due to the lack of experimental data and technical knowledge, the licensing challenges for non-water coolant SMRs are more complicated. Nearly all previous generation reactor licenses were based on conservative analysis while the decision-making methods based on best-estimate and realistic approaches have received more attention in recent years. Thus, the method known as the best estimate plus uncertainty (BEPU) approach is selected for licensing in some cases. At this time, using the BEPU approach in licensing for conventional NPPs is a mature technology and ready for industrial application. Nevertheless, because most previous reactors were licensed based on conservative methods, developers and even regulatory bodies resist re-assessments based on the BEPU approach, while using the choice of conventional conservative methods is a type of roll-back for next-generation SMRs. Thus, this work reviews the BEPU approach and clarifies the possibility of using this approach in the licensing process of SMRs. The lack of experimental data and tight coupling of phenomena along with uncertainty quantification are the main challenges ahead of using BEPU in the licensing process of SMRs.

Extension of the CIRCE methodology to improve the Inverse Uncertainty Quantification of several combined thermal-hydraulic models

The Inverse Uncertainty Quantification (IUQ) of physical correlations used in thermal-hydraulic system codes is a crucial issue in the BEPU (Best Estimate Plus Uncertainty) framework for the licensing and safety analyses of nuclear reactors. The CIRCE methodology is one of the most widely applied IUQ methods. It estimates the (log-)normal probability distribution of a multiplicative factor applied to the reference closure model used in thermal-hydraulic computer codes. CIRCE can jointly estimate the uncertainty of several physical models. However, in some particular cases, a problem of identifiability may occur resulting in less accuracy and precision of the estimated uncertainties.For this reason, in this work, the methodology is improved under the name of CIRCE 2-Steps. This new approach aims at improving the quantification of the model uncertainties when experiments with more than one physical phenomena interacting simultaneously on the output of interest has to be used. In a first step, the uncertainties of the least influential models are evaluated with classic CIRCE methodology using experiments for which only one physical phenomenon is dominant. Then, these uncertainties are properly taken into account when quantifying the remaining uncertainties on the experimental database. This approach is proven to provide more accurate and precise results on several analytical test cases where the uncertainties of two models has to be jointly estimated. The study of the impact of the relative importance of the two models shows that the biggest gain in precision is obtained when the hierarchy of models is such that one model is significantly more influential than the other.Finally, the newly developed methodology is applied to estimate the uncertainties of two condensation heat transfer correlations in the cold leg of a pressurised nuclear reactor.

BEPU Analyses for the Postulated Loss-of-cooling Accident Scenario in the Spent Fuel Pool at the Fukushima Daiichi Unit 4

The aim of the paper is to present the results obtained from the study devoted on the Best Estimate plus Uncertainty (BEPU) Methods application. To this end, the simulation of the Loss of cooling accident (LOCA) scenario in the Fukushima Daiichi spent fuel pool was carried out. Special attention was paid on the uncertainty analysis with the domain fission products release. The work presented herein was carried out by using the ASTECv2.2b/SUNSET in the coupling mode. A brief description of the ASTECv2.2b/SUNSET coupling is provided and a short discussion concerning the BEPU methodology is also presented.

CTF-PARCS Core Multi-Physics Computational Framework for Efficient LWR Steady-State, Depletion and Transient Uncertainty Quantification

Best Estimate Plus Uncertainty (BEPU) approaches for nuclear reactor applications have been extensively developed in recent years. The challenge for BEPU approaches is to achieve multi-physics modeling with an acceptable computational cost while preserving a reasonable fidelity of the physics modeled. In this work, we present the core multi-physics computational framework developed for the efficient computation of uncertainties in Light Water Reactor (LWR) simulations. The subchannel thermal-hydraulic code CTF and the nodal expansion neutronic code PARCS are coupled for the multi-physics modeling (CTF-PARCS). The computational framework is discussed in detail from the Polaris lattice calculations up to the CTF-PARCS coupling approaches. Sampler is used to perturb the multi-group microscopic cross-sections, fission yields and manufacturing parameters, while Dakota is used to sample the CTF input parameters and the boundary conditions. Python scripts were developed to automatize and modularize both pre- and post-processing. The current state of the framework allows the consistent perturbation of inputs across neutronics and thermal-hydraulics modeling. Improvements to the standard thermal-hydraulics modeling for such coupling approaches have been implemented in CTF to allow the usage of 3D burnup distribution, calculation of the radial power and the burnup profile, and the usage of Santamarina effective Doppler temperature. The uncertainty quantification approach allows the treatment of both scalar and functional quantities and can estimate correlation between the multi-physics outputs of interest and up to the originally perturbed microscopic cross-sections and yields. The computational framework is applied to three exercises of the LWR Uncertainty Analysis in Modeling Phase III benchmark. The exercises cover steady-state, depletion and transient calculations. The results show that the maximum fuel centerline temperature across all exercises is 2474K with 1.7% uncertainty and that the most correlated inputs are the 238U inelastic and elastic cross-sections above 1 MeV.

Determination of heat flux leading to the onset of flow instability in MTR reactors

Abstract The prediction of heat flux leading to the Onset of Flow Instability (OFI) phenomena is an important consideration in the design of Material Testing Reactors (MTR) due to the possibility of flow excursion during postulated accident. From the thermal-hydraulic point of view, OFI is the critical phenomenon limiting MTR reactor power. In a previous work, an empirical correlation is developed to predict the subcooling at OFI in narrow vertical rectangular channels simulating a coolant channel of MTR. In the present work, an innovative model to determine the heat flux leading to OFI in MTR reactors is introduced based on the previous correlation. The developed model gives a very low deviation of only 1.65% from the experimental data of Whittle & Forgan that covers a wide range of MTR operating conditions. The heat flux leading to OFI is also predicted by both Whittle & Forgan and Fabrega correlations for comparison. The present model is then applied on the IAEA 10 MW MTR generic reactor to predict the Best-Estimate (BE) and Best-Estimate-Plus-Uncertainty (BEPU) Onset of Flow Instability Ratio (OFIR) and the power leading to OFI as well as the bubble detachment parameter under different coolant velocities and inlet temperatures. The model is also used to predict both the OFIR and bubble detachment parameter in the reactor under unprotected Loss-of-Flow transient for exponential flow decay with a time constant of 1.0 s (fast LOFA), 10, 15 and 25 s (slow LOFA) from a power level of 10 MW. For BEPU calculation, a combined statistical method with direct propagation of errors is adapted to treat the uncertainty factors for fuel fabrication and measured parameters in the BEPU calculation. The model results is analyzed and discussed.

Application of Best Estimate Plus Uncertainty (BEPU) Methodology in a Final Safety Analysis Report (FSAR) of a Generic Plant

The licensing process of a nuclear power plant is motivated by the need to protect humans and the environment from ionizing radiation and, at the same time, sets out the basis for the design and determining the acceptability of the plant. An important part of the licensing process is the realization of accident analysis related to the design basis, which should be documented in the Final Safety Analysis Report (FSAR). There are different options on accidents calculation area by combining the use of computer codes and data entry for licensing purposes. One is the Best Estimate Plus Uncertainty (BEPU), which considers realistic input data and associated uncertainties. Applications of BEPU approaches in licensing procedures were initiated in the 2000s, first to analysis of Loss of Coolant Accident (LOCA), and then to the accident analysis as a whole, documented in Chapter 15 of the FSAR. This work has as main objective the implementation of BEPU methodology in all analyses contained in FSAR, through the homogenization of the analytical techniques and identification of key disciplines and key topics in the licensing process.

Severe accident sensitivity and uncertainty estimation using MELCOR and RAVEN

Today, using a best-estimate approach is a key factor in the simulation and prediction of thermal-hydraulic and other multi-physics phenomena occurring during nuclear severe accidents. The best-estimate approach requires the quantification of both epistemic and stochastic uncertainties of safety codes to be effective. This safety assessment approach, named Best Estimate Plus Uncertainty (BEPU), is being pursued as an alternative to traditional deterministic analyses that are intrinsically conservative with not clearly defined safety margins. While in a conservative approach, the results are expressed in terms of a set of calculated conservative values of parameters, in a best-estimate methodology, the results are expressed in terms of uncertainty ranges for the calculated parameters. The International Technical Nuclear Community has made great efforts to develop methods and tools for uncertainty and sensitivity analyses of severe accident codes. In this framework, Sapienza University of Rome has developed a new Python script to use RAVEN as a tool for the application of the BEPU methods within the safety analyses performed with MELCOR. The aim of this paper is to show the capabilities of the coupling between RAVEN and MELCOR by performing a statistical analysis to estimate the range of evolution of a severe accident scenario.

A comprehensive Bayesian framework for the development, validation and uncertainty quantification of thermal-hydraulic models

The development, validation and uncertainty quantification of closure laws used into thermal–hydraulic system codes is a key issue before applying the BEPU (Best Estimate Plus Uncertainty) methodology for safety studies and licensing of nuclear reactors. The assessment of those physical models requires tuning some parameters against available experimental data. This paper presents a methodology called Bayesian calibration, which allows a more robust and reliable assessment, selection and uncertainty quantification of physical models.In this work, the experimental and predicted values are linked by means of a multiplicative random variable which represents the model uncertainty. This hypothesis is suitable for models scaling across many orders of magnitude as it is the case in nuclear thermal–hydraulic. Several empirical models, which describe the same physics with different formalisations, are calibrated. Then, the one which is the best-suited according to different statistical indicators is selected. A statistical validation is performed with a Leave One Out (LOO) technique which allows using the same database for both assessment and validation of the physical model. Finally, the uncertainty on the selected best-fitting model is assessed.This framework is applied to condensation heat transfer correlations for safety injection based on the COSI (COndensation at Safety Injection) experiments.

Uncertainty Study of the In-Vessel Phase of a Severe Accident in a Pressurized Water Reactor

A comprehensive uncertainty analysis in the event of a severe accident in a two-loop pressurized water reactor is conducted using an uncertainty package integrated in the ASYST code. The plant model is based on the nuclear power plant (NPP) Krško, a Westinghouse-type power plant. The station blackout scenario with a small break loss of coolant accident is analyzed, and all processes of the in-vessel phase are covered. A best estimate plus uncertainty (BEPU) methodology with probabilistic propagation of input uncertainty is used. The uncertain parameters are selected based on their impact on the safety criteria, the operation of the NPP safety systems and to describe uncertainties in the initial and boundary conditions. The number of required calculations is determined by the Wilks formula from the desired percentile and confidence level, and the values of the uncertain parameters are randomly sampled according to appropriate distribution functions. Results showing the thermal hydraulic behaviour of the primary system and the propagation of core degradation are presented for 124 successful calculations, which is the minimum number of required calculations to estimate a 95/95 tolerance limit at the 3rd order of the Wilks formula application. A statistical analysis of the dispersion of results is performed afterwards. Calculation of the influence measures shows a strong correlation between the decay heat and the representative output quantities, which are the mass of hydrogen produced during the oxidation and the height of molten material in the lower head. As the decay heat increases, an increase in the production of hydrogen and the amount of molten material is clearly observed. The correlation is weak for other input uncertain parameters representing physical phenomena, initial and boundary conditions. The influence of the order of the Wilks formula is investigated and it is found that increasing the number of calculations does not significantly change the bounding values or the distribution of results for this particular application.